This document discusses time, dose, and fractionation in radiation therapy. It begins by introducing the aims of delivering precisely measured radiation doses to tumors while minimizing damage to normal tissues. It then discusses tumor lethal dose, tissue tolerance factors, and how normal tissue tolerance limits the maximum dose that can be delivered. The document covers dose, time, and fractionation as treatment factors. It reviews several historical time-dose models including Strandquist lines, Cohen's model, Fowler's work, Ellis' NSD equation, and the linear quadratic model which is still commonly used today. It also notes limitations of some early empirical models.

1. Time Dose & Fractionation
Relationship
Prof Amin E A Amin
Dean of the Higher Institute
of Optics Technology
Prof of Medical Physics
Radiation Oncology Department
Faculty of Medicine
Ain Shams University

2. INTRODUCTION
• To deliver precisely measured dose of radiation to a defined
tumor volume with minimal damage to surrounding normal
tissue.
• Aims:
– To eradicate tumor,
– Improve quality of life &
– Prolongation of survival.

3. TUMOR LETHAL DOSE
• Dose of radiation that produces complete & permanent
regression of tumor in vivo in zone irradiated.

4. TISSUE TOLERANCE
• Radiation dose that will not produce any
appreciable damage to normal tissue irradiated.
• Usually <5% damage to normal tissue is
acceptable.
• In RT the success of eradicating tumor
depends on radiosensitivity of tumor as well as
tolerance of surrounding normal tissue

5. TISSUE TOLERANCE
• Normal Tissue Tolerance (NTT) limits the
max. dose that can be delivered to tumor.
• During early years of RT with orthovoltage
skin was a limiting factor.
• This was overcome by use of Co-60 &
megavoltage X-rays .

6. NTT: Factors
• Site of tissue – axilla, perineum less tolerant
• Area or volume irradiated
• Vascularity
• Supporting tissues (stroma and parenchymal cells)
• Individual variation of tolerance.

7. TREATMENT FACTORS
• To eradicate a tumor radiation is delivered & factors that play
an important role in any treatment are
– Dose of radiation
– Time of dose delivery
– Fractionation of dose

8. DOSE
• Is a physical quantity
• Amount of energy absorbed from beam of
radiation at a given point in medium.

9. CHOICE OF DOSE
• In radical radiotherapy choice of dose & fractionation
regimen depends on following factors:-
– Radio sensitivity of tumor –
• e.g. radiosensitive tumor such as seminoma can be
controlled by total dose of 30Gy/ 4wks
• While for moderately sensitive sq. cell ca. of head &
neck higher doses of the order of 50-60Gy in 5-6wks
is used

10. CHOICE OF DOSE
– Size of treatment volume –
• smaller the vol. the greater is the dose that can be
delivered without exceeding NTT.
– Proximity of dose limiting structures –
• presence of critical structure such as brain stem &
spinal chord may limit dose that can be delivered to
tumors e.g. while treating head & neck cancer &
esophagus spinal chord is the critical structure.

11. CHOICE OF DOSE
• To assess the effects of quantity of radiation following
doses should be known for clinical purposes :-
• Given dose – The dose being delivered by any one
beam either to an area of skin for KV beam or to the
level of max. buildup below the skin for MV beam.
• Tumor dose – The dose (max. or min.) being delivered
in selected treated zone containing tumor i.e. tumor &
safety margins.

12. CHOICE OF DOSE
• Skin dose – The actual dose received by any area of skin
summating given dose contributions received through body
from any beam.
• Sub lethal dose – Dose which results in only temporary
shrinkage of tumor having rarely palliative value if any and
with no lethal effect.

13. CHOICE OF DOSE
• Supra lethal dose - dose to tumor which gives a slow
response giving rise to an indurate mass with sloughing
of tumor centre & ultimately frequent recurrences at a
later date. (dose above lethal level).
• Integral dose – Total amount of energy absorbed at each
and every point inside treatment volume. It should be
minimum provided adequacy of tumor irradiation &
sparing of critical organs are not compromised.

14. TIME
• Time factor is overall time to deliver prescribed dose from
beginning of course of radiation until its completion.
• Therapy effect varies enormously with time.
• General rule is longer the overall duration of treatment
greater is the dose required to produce a particular effect.
• Hence dose should always be stated in relation to time.

15. TIME
• For curative purposes overall treatment is 5-6wks
– Better tumor control with minimal morbidity
– Tumor suppression can be monitored.
– Radiation reactions can be monitored.
• If treatment time is more than 6wks then dose has to be increased
• Short duration treatment time is justified for
– Treatment of small lesions
– To treat aged persons
– Palliative treatments
– Tumors with high therapeutic ratio e.g. skin tumors

16. FRACTIONATION
• Refers to division of total dose into number of separate
fractions over total treatment time conventionally given on
daily basis , usually 5days a wk.
• Size of each dose per fraction whether for cure or palliation
depends on tumor dose as well as normal tissue tolerance .
• e.g. if 40Gy is to be delivered in 20# in a time of 4wks then
daily dose is 2Gy.

17. HISTORICAL REVIEW
• X-ray were used for radiotherapy just 1 month after its
discovery in a fractionated course because of the primitive
X-ray machines available at that time & their low output
• To deliver a single dose to destroy a tumor would require
several hours or even days.
• Single fraction radiotherapy became feasible only in 1914
with the advent of Coolidge hot cathode tube, with high
output, adjustable tube currents & reproducible exposures.

18. HISTORICAL REVIEW
• Earlier some radiotherapists believed that
fractionated treatment was inferior &
single dose was necessary to cure cancer.
• While radiobiological experiments
conducted in France favored fractionated
regimen for radiotherapy which allows
cancerocidal dose to be delivered without
exceeding normal tissue tolerance.

19. RADIOBIOLOGICAL RATIONALE FOR
FRACTIONATION
• Delivery of tumorocidal dose in small dose fractions in
conventional multifraction regimen is based on 4R’s of
radiobiology namely
– Repair of SLD
– Repopulation
– Redistribution
– Reoxygenation
• Radio sensitivity is considered by some authors to be 5th
R of radiobiology.

20. ADVANTAGES OF FRACTIONATION
• Acute effects of single dose of radiation can be decreased
• Pt.’s tolerance improves with fractionated RT
• Exploits diff. in recovery rate between normal tissues &
tumors.
• Radiation induced redistribution & sensitization of rapidly
proliferating cells.
• Reduction in hypoxic cells leads to –
– Reoxygenation
– Opening of compressed blood vessels
• Reduction in no. of tumor cells with each dose fraction

21. TIME DOSE MODELS
• With introduction of various fractionation schemes in
radiotherapy need for quantitative comparisons of
treatments was felt in order to optimize treatment for
particular tumor.

22. Strandquist Lines
• In 1944 Strandquist was the first to device a
scientific approach for correlating dose to
overall treatment time to produce an
equivalent biological isoeffect.
• For skin and connective tissue tolerance he
plotted the logarithm of dose vs. log time
and obtained straight lines.
• These lines are called Strandquist lines

23. Strandquist Lines
A: skin necrosis
B: cure of skin
carcinoma
C; moist desquamation
D: dry desquamation
E; erythema

24. Strandquist Lines

25. Cohen’s Model
• In 1949 Cohen suggested the slope of the lines
as 0.33 and 0.22 for normal and cancer tissues
respectively.

26. Power Empirical Models
• This gave the relationship between the tolerance dose and the
time in which it was delivered as
• Where
Dn and Dt are doses to normal tissue and tumour,
K1 and K2 are constants,
T is the overall treatment time,
For normal tissue and tumour control respectively.
22.0
2
33.0
1
TKD
TKD
t
n
=
=

27. Fowler
• Difference in exponents of time factor
in Cohen’s formulations indicate that
repair capacity of normal tissue is
larger than that of tumor.

28. Fowler
• Fowler carried experimental studies on pig skin showing
normal tissue have two type of repair capabilities
– Intracellular – having short repair half time of 0.5 to 3hrs & is
complete within few hrs of irradiation. Multiplicity of completion of
recovery is equal to no. of fractions.
– Hence number of fractions are more important than overall treatment
– Homeostatic recovery that takes longer time to complete
• This led Ellis to formulate NSD

29. Power Empirical Models
• The exponents of T in the equations represent the average
values of repair and recovery capacities of normal and
tumour tissues.
• Ellis found this repair for normal cells larger than that for
tumour and attributed this to lack of homeostatic control in
case of malignant tumours.
• It was further assumed by Ellis that the homeostatic
recovery was a long term recovery and the intracellular
recovery was of short term nature.

30. Ellis NSD Equation
• Ellis , in 1967, used the iso-effect data for
skin from Strandquist and proposed the the
tolerance dose for normal tissues (D rads)
was related to overall treatment time (T
days) and the number (N) of fractions.
• Where NSD = Nominal standard dose (rets)
11.024.0
11.024.0
)(
−−
=
=
TDNNSD
TNNSDD

31. Cumulative Radiation Effect
• Ellis defined the NSD concept at the tolerance of normal
tissues. He described NSD formula where N was the
number of fractions that result in tolerance of normal tissue
and T was the corresponding treatment time.
• Assuming n be any number of fractions not necessarily
resulting in normal tissue tolerance but into a subtolerance
reaction and t be the corresponding treatment period, Kirk
gave the expression for Cumulative Radiation Effect (CRE)
as
11.024.0 −−
= tDnCRE

32. Cumulative Radiation Effect
• Kirk and his colleagues concluded that the CRE formula was
identical and numerically equal with the NSD formula at the
limit of normal connective tissue tolerance.

33. Partial Tolerance
• NSD/CRE concepts were wrongly used by adding the numerical
values of the individual schedules.
• Radiotherapists particularly found these difficult to use.
• A concept of partial tolerance (PT) was defined by Ellis as:
Where n was stated as any number of fractions of a schedule
and N were the ones resulting in normal tissue tolerance.
N
n
NSDPT =

34. Time Dose Fractionation Factor
• Using the expression for partial tolerance, Orton and Ellis
developed a new factor called “Time Dose Fractionation (TDF)
factor” which was directly proportional to the number fo
fractions and hence to the dose given in a treatment.
• Where x= t/n
• The term 10-3 was used by them so that the numerical values of
TDF are around 100, not very large and so as to facilitate
handling of numerical values of the concept.
3169.0538.1
10−−
= nxdTDF

35. Limitations of Power Empirical
Models
• In 1988 Orton and Cohen had summarized the limitations of the
power empirical models as follows:
1. These formulae do not take into account all the complex
biological processes that take place during and/or after the
course of irradiations. Hence, the formulae are merely intended
to provide radiotherapists with a simple and convenient method
based on clinical experience of relating total dose, number of
fractions and overall treatment time.

36. Limitations of Power Empirical
Models
2. Serious doubt have been raised concerning the validity of NSD
relation with respect to the type of tissue involved. Available
evidence indicates that for different tissues the dependence of
tolerance doses on fractionation schedules is not the same.
Values of the exponent of N in the NSD formula has been
reported to range from 0.2 to 0.5.

37. Limitations of Power Empirical
Models
3. The validity of the NSD with respect to different effects in the
same tissue or organ is doubtful. Clinical as well as
radiobiological data indicate that for late effects in skin the
influence of the number of fractions may be considerably
larger than for acute skin responses. More late damage was
observed for small number of fractions than expected on the
basis of the NSD formula.

38. Limitations of Power Empirical
Models
4. A further uncertainty relates to the range of number of
fractions for which the formulae provide a reasonable
approximation of the tolerance dose of a given tissue. It has
suggested that for effects in skin a sufficient approximation is
obtained only between 10 and 25 fractions.

39. Limitations of Power Empirical
Models
5. An important difficulty concerned is the time factor T0.11. The
factor suggests an increase in dose required to compensate the
repair by approximately 20% in the first week about 10% in the
second week and about 5% in the third week. For acute reactions
in skin and mucosa. Accelerated repopulation is probably an
important factor but this is known to start only after two of three
weeks of fractionated treatments. For tissues with a low rate of
cell renewal, i.e., those which would show late injury, cell
proliferation during the 4-8 weeks of treatment as commonly
applied in radiotherapy is not expected to increase the tolerance
as much as predicted by the NSD formula.

40. Neuro-Ret Model
• In spite of the original intentions to use new
fraction-number factors as new data came in,
the only significant introduction has been that
of the "neuro-ret", with an exponent of 0.4
instead of 0.24 for fraction number.

41. Linear Quadratic Model
• The biophysical justification of the linear
quadratic (LQ) model was proposed as a
consequence of the microdosimetry of radiation
cellular lesions.

42. Linear Quadratic Model
• The linear term results from the interaction of
lesions that occur along a single ionizing track
while the quadratic term results from the
interaction of lesions occurring along two
different particle tracks.

43. Linear Quadratic Model
• The LQ model could be used to prdict
the improvement in therapeutic ratio by
careful adjustment of dose per fraction.
BARENDSEN, G.W.

44. LQ Model Assumptions
• The model is based upon the apparent linear quadratic
shape of cell survival curve for which there is
radiobiological and physical support.
• Following basic assumptions are generally considered in
developing LQ model to radiotherapy:

45. LQ Model Assumption 1
• Ionizing radiations produce lesions in cells.
• Part of radiation causes directly effective lesions with a
frequency increasing linearly with the absorbed dose.
• Other lesions, are called subeffective lesions, can cause the
same cellular effect through mutual interaction among
themselves, these effects increase with the square of the
absorbed dose.

46. LQ Model Assumption 2
• The effective lesions which increases with the square of
the dose, result from interaction of subeffective lesions,
requiring close enough to each other in space and in time
in the same cells.

47. LQ Model Assumption 3
• The subeffective lesions remain available for interaction
during a limited time interval after their production.
• The decay of their capacity for interaction is assumed to
be an exponential function, characterized by a half life of
0.5 to 4 hrs.

48. LQ Model Assumption 4
• The effectiveness of a given dose fraction of a treatment
regimen for the commonly applied schedules assumed to be
NOT significantly dependent on changes in the sensitivity of
cells as a function of their proliferative status and of their
position in mitotic cycle, i.e., for the present analysis the
fraction of resting cells and the cell synchronization are
considered to be not important in the treatment considered.
• This assumption implies that equal dose fractions are equally
effective, independent of the preceding or following dose
fractions.

49. LQ Model Assumption 5
• A response of a tissue results from the induction of effects
in cells and requires the average number of effective
lesions, in irradiated cells to attain a particular value, which
depends on the response considered.
• If the integrity and the function of a tissue is determined by
the capacity for unlimited proliferation of the constituent
cells, this level of injury corresponds to a specific fraction
of surviving cells.

50. LQ Model Assumption 5
• The response level can be attained as a consequence of a single
dose or of a series of fractionated irradiations.
• The time intervals between the fractions are large enough to
allow complete repair or decay of sublethal damage.

51. LQ Model Assumption 5
• For the induction of a specific tissue response, the number of
cellular effective lesions at the end of a treatment is the
determining parameter.
• As a consequence, the total dose required for a given tissue
response is inversely proportional to the effectiveness with
which the cellular effects are induced.

52. LQ Model Assumption 6
• The influence of cell proliferation during protracted treatment
regimen must be accounted for separately for each type of
tissue.

53. LQ Model
• The surviving fraction (SFd) of target cells after a dose per
fraction d is as:
• SFd = exp(-αd - βd2)

54. LQ Model
• Cell Kill = 1 – SF
• Ln(Cell Kill) = -Ln(SF)
• E = Ln(Cell Kill) = -Ln(SF)

55. LQ Model
• Radiobiological studies have shown that each successive
fraction in a multidose schedule is equally effective, so
the effect (E) of n fractions can be expressed as:
E = -ln(SFd)n = -n ln(SFd)
= n(αd + βd2)
= αD + βdD
where the total radiation dose D = nd.

56. LQ Model
• The above equation may be rearranged into the
following forms:
• E/α = D[1 + d/ (α /β)]
• = n[d + d2/ (α /β)]

57. LQ Model
• For isoeffect in a selected tissue, E and α are constant.
• A schedule employs a dose per fraction d1 and the
isoeffective total dose is D1; we change to a dose per fraction
d2 and the new (unknown) total dose is D2.
• D2 is related to D1 by the equation:
• This simple LQ isoeffect equation was first proposed by
Withers et al. in 1983.
• It has widely been found to be successful in clinical
calculations.
)/(
)/(
2
1
1
2


+
+
=
d
d
D
D

58. Estimation of α/β Ratio
• 1/D = (α/E) + (β/E)d
• By plotting 1/D against d, for
isoeffective schedules, we can
estimate the value of /.

59. The Values of the α/β ratio
• It is important to recognize that the α/β ratio is not constant and
its value should be chosen carefully to match the specific tissue
under consideration.

60. The Values of the α/β ratio
• Acute responding tissues
• For acutely responding tissues which express their damage
within a period of days to weeks after irradiation, the α/β ratio is
in the range 7–20Gy.

61. The Values of the α/β ratio
• Late responding tissues
• For late-responding tissues, which express their damage months
to years after irradiation, α/β generally ranges from 0.5 to 6Gy.

62. The Values of the α/β ratio
Values of the α/β ratio for
a range of human normal
tissues and tumours

63. The Values of the α/β ratio
Values of the α/β
ratio for a range of
human normal
tissues and tumours

64. The Values of the α/β ratio
Values of the α/β
ratio for a range of
human normal
tissues and tumours

65. The Values of the α/β ratio
Values of the α/β
ratio for a range of
human normal
tissues and tumours

66. EQUIVALENT DOSE IN 2-GY
FRACTIONS (EQD2)
• The LQ approach leads to various formulae for calculating
isoeffect relationships for adiotherapy, all based on similar
underlying assumptions.
• These formulae seek to describe a range of fractionation schedules
that are isoeffective.
• The simplest method of comparing the effectiveness of schedules
consisting of different total doses and doses per fraction is to
convert each schedule into an equivalent schedule in 2-Gy
fractions which would give the same biological effect.

67. EQUIVALENT DOSE IN 2-GY
FRACTIONS (EQD2)
• This is the approach that has been recommend
as the method of choice and can be achieved
using a specific version of equation
)/(2
)/(
)/(
)/(
)]/([)]/([
2
2
1
12
2211





+
+
=
+
+
=
+=+
d
DEQD
then
d
d
DD
dDdD

68. EQUIVALENT DOSE IN 2-GY
FRACTIONS (EQD2)
• EQD2 is the dose in 2-Gy fractions that is
biologically equivalent to a total dose D given
with a fraction size of d Gy.
)/(2
)/(
2


+
+
=
d
DEQD

69. EQUIVALENT DOSE IN 2-GY
FRACTIONS (EQD2)
• Values of EQD2 may be numerically added for separate
parts of a treatment schedule.
• They have the advantage that since 2Gy is a commonly
used dose per fraction clinically, EQD2 values will be
recognized by radiotherapists as being of a familiar size.

70. Example
• Calculate value of EQD2 which is isoeffective to the
schedule of 30Gy/10F for tumour having / = 20 Gy.
• Soluttion
GyEQD
d
DEQD
4.31
22
23
30
202
203
30
)/(2
)/(
2
2
==
+
+
=
+
+
=



71. Example
• Calculate value of EQD2 which is isoeffective to the
schedule of 30Gy/10F for tumour having / = 10 Gy.
• Soluttion
GyEQD
d
DEQD
5.32
12
13
30
102
103
30
)/(2
)/(
2
2
==
+
+
=
+
+
=



72. Example
• Calculate value of EQD2 which is isoeffective
to the schedule of 30Gy/10F for late
responding tissue having / = 3 Gy.
• Soluttion
GyEQD
d
DEQD
36
5
6
30
32
33
30
)/(2
)/(
2
2
==
+
+
=
+
+
=



73. Example
• Calculate value of EQD2 which is isoeffective to the
schedule of 30Gy/10F for late responding tissue having
/ = 2 Gy.
• Soluttion
GyEQD
d
DEQD
5.37
4
5
30
22
23
30
)/(2
)/(
2
2
==
+
+
=
+
+
=



74. Effect of / Ratio
• If we compare the results of the previous examples we may
notice that the value of / ratio has a great effect on the result
and the effect is higher for lower of / ratio.

75. The Biologically Effective Dose (BED)
• BED is a measure of the effect (E) of a course of fractionated
or continuous irradiation; when
• divided by α it has the units of dose and is usually expressed
in grays (Gy).






+=
+=
+=
=






/
ddN
]d)(N[d
][
N
/EBED
2
2
2
dd

76. The Biologically Effective Dose
(BED)
• Note that as the dose per fraction (d) is reduced towards zero,
BED becomes D = nd (i.e. the total radiation dose).
• Thus, BED is the theoretical total dose that would be required
to produce the isoeffect E using an infinitely large number of
infinitesimally small dose fractions.
• It is therefore also the total dose required for a single
exposure at very low dose rate.

77. The Biologically Effective Dose (BED)
• As with the simpler concept of EQD2, values of BED from
separate parts of a course of treatment may be added in order to
calculate the overall BED value..

78. The Biologically Effective Dose (BED)
• A disadvantage of BED as a measure of treatment intensity is
that it is numerically much greater than any prescribable
radiation dose of fractionated radiotherapy and is therefore
difficult to relate to everyday clinical practice, which is the
main reason why it is recommended to use EQD2.

79. The Biologically Effective Dose (BED)
• It is also convention to express BED in units of Gyα/β to
indicate the effects to which the result apply. It is not
meaningful to add the BED of partial acute effects (e.g. Gy10) to
the BED for partial late reactions (e.g. Gy3).

80. Total effect
• The total effect (TE) formulation is conceptually
similar to BED.
• In this case, we divide E by β rather than α, to get
E/β = D[(α/β) + d] = TE
• The units of TE are Gy2,which again means that
the TE values have no simple interpretation.

81. BIOLOGICAL EFFECT DOSE
• Standard Radiation:
76 Gy in 38 fractions in 2.0 Gy per fraction
Rectum BED4=76 ( 1 + 2/4 ) =114
Tumor BED1.5=76 ( 1 + 2/1.5 ) =177.3
• Hypofractionated Radiation:
70.2 Gy in 26 fractions in 2.7 Gy per fraction
Rectum BED4=70.2 ( 1 + 2.7/4 ) =118
Tumor BED1.5=70.2 ( 1 + 2.7/1.5 ) =197

82. BIOLOGICAL EFFECT DOSE
• Standard Radiation:
76 Gy in 38 fractions in 2.0 Gy per fraction
Rectum BED4=76 ( 1 + 2/4 ) =114
Tumor BED10=76 ( 1 + 2/10 ) =91
• Hypofractionated Radiation:
70.2 Gy in 26 fractions in 2.7 Gy per fraction
Rectum BED4=70.2 ( 1 + 2.7/4 ) =118
Tumor BED10=70.2 ( 1 + 2.7/10 ) =89

83. VARIOUS FRACTIONATION
SCHEDULES
• Fractionated radiation exploits difference in 4R’s between
tumors and normal tissue thereby improving therapeutic
index
• Types
– Conventional
– Altered
• Hyper fractionation
• Accelerated fractionation
• Split course
• Hypofractionation

84. CONVENTIONAL FRACTIONATION
• Division of dose into multiple fractions spares normal tissue
through repair of SLD between dose fractions & repopulation
of cells. The former is greater for late reacting tissues & the
later for early reacting tissues.
• Concurrently, fractionation increases tumor damage through
reoxygenation & redistribution of tumor cells.
• Hence a balance is achieved between the response of tumor &
early & late reacting normal tissue.
• Most common fractionation for curative radiotherapy is 1.8 to
2.2Gy/fraction.

85. CONVENTIONAL FRACTIONATION
• Evolved as conventional regimen because it is
– Convenient (no weekend treatment)
– Efficient (treatment every weekday)
– Effective (high doses can be delivered without exceeding
either acute or chronic normal tissue tolerance)
– Allows upkeep of machines.
• Rationale for using conventional fractionation
– Most tried & trusted method
– Both tumorocidal & tolerance doses are well documented

86. HYPERFRACTIONATION
• Hyperfractionation – smaller fractions, given 2 or 3 times a
day, same overall time
• Reduces late effects for same or better tumor control and
same or slightly increased early damage
• To take maximal advantage of difference in repair capacity of
late reacting normal tissue compared with tumors.
• Radio sensitization through redistribution.

87. ACCELERATED TREATMENT
• Accelerated fractionation – shorten overall treatment time by
giving 2 or 3 fractions a day, keeping total dose and fraction
size similar to conventional
• Increase tumor control in rapidly growing tumors by giving
dose in a shorter time

88. HYPOFRACTIONATION
• Hypofractionation – larger fractions to improve therapeutic ratio
where tumours have lower α/β than late-responding normal tissue
• Treatment completed in a shorter period of time.
• Machine time well utilized for busy centers.
• Higher dose /fraction gives better control for larger tumors.
• Higher dose /fraction also useful for hypoxic fraction of large
tumor.
• Disadvantage: Higher potential for late normal tissue
complications.

89. CHART
• CHART – Continuous Hyperfractionated Accelerated
Radiotherapy
• 3 fractions/day; 6 hours between fractions; 7daya a wk. with
fraction size of 1.5Gy, total dose of 54Gy can be delivered in
36fractions over 12 consecutive days including weekends.
• This schedule was chosen to complete treatment before acute
reactions start appearing i.e. 2wks.

90. SPLIT-COURSE
• Total dose is delivered in two halves with a gap in between
with interval of 4wks.
• Purpose of gap is
– to allow elderly patients to recover from acute reactions of treatment
– to exclude patients from further morbidity who have poorly tolerated
1st half or disease progressed despite treatment.
• Applied to elderly pts. in radical treatment of ca bladder &
prostate & lung cancer.
• Disadv : impaired tumor control due to prolong T/T time that
results in tumor cell repopulation

91. Concomitant boost
▪ Boost dose to a reduced volume given concomitantly , with
treatment of initial layer volume
▪ Conv 54Gy in 30 # over 6 wks & boost dose of 1.5 Gy per #
in last 12 # with Inter # interval of 6 hr in last 12#
▪ large field gets 54 Gy & boost field 72 Gy in 6 wks time
▪ E.g. Head and Neck cancer

92. conventional
Hyper fractionation
Accelerated fractionation
Concomitant boost
Split - course
Hypo fractionation

93. LQ Model
• Deviding both sides by , then
If we have two Isoeffective schedules i.e. having
the same E, then
)( 2
ddNE  +=
)( 2
ddN
E
+=



)(
)(
)()(
2
22
2
111
2
2
222
2
111
dd
ddN
N
Then
ddNddN
+
+
=
+=+









94. Example
• What is the hypofractionation schedule (with fraction Size
3Gy) equivalent to 50cGy/25F/5w for late responding
tissue with / = 2 Gy
• Solution
D= 13 x3=39Gy i.e. the schedule is 39Gy/13F/5w
13
15
200
96
825
)932(
)422(25
)(
)(
2
2
22
2
111
2
==
+
=
+
+
=
+
+
=
x
x
x
N
dd
ddN
N





95. Example
• What is the hypofractionation schedule (with fraction Size 3Gy)
equivalent to 50cGy/25F/5w for for tumour with / = 10 Gy
• Which of them has the higher effect on spinal cord if its / = 2
Gy.
• Give the reason of the result.

96. Example
• Solution
D= 15 x3=45Gy i.e. the schedule is 45Gy/15F/5w
EQD2=45[(3+2)/(2+2)]=45(5/4)=56Gy2
15
39
600
930
2425
)9310(
)4210(25
)(
)(
2
2
22
2
111
2
==
+
=
+
+
=
+
+
=
x
x
x
N
dd
ddN
N





97. EXTENSION OF LQ MODEL
TO INCLUDE TIME:
• In 1988 Wheldon & Amin extended
the LQ model to include a time
factor. We suggested to
formulations the simplest form was;
• E = - ln S = n(αd + βd2) - γT
• γ equals ln2/Tp with Tp the potential
doubling time.

98. EXTENSION OF LQ MODEL
TO INCLUDE TIME:
• Note that the γT term has the opposite sign to the α + βd term
indicating tumour growth instead of cell kill

99. THE POTENTIAL DOUBLING TIME
• The fastest time in which a tumour can double its volume
• Depends on cell type and can be of the order of 2 days in fast
growing tumours
• Can be measured in cell biology experiments
• Requires optimal conditions for the tumour and is a worst case
scenario

100. EXTENSION OF LQ MODEL TO
INCLUDE TIME:
• The other form we have suggested is
• E = - ln S = n(α d+ βd2) – γ(T-Tk)
• Including Tk ("kick off time") which allows for a time lag
before the tumour switches to the fastest repopulation time:
• BED = (1 + d / (α/β)) * nd - (ln2 (T - Tk)) / αTp

101. TREATMENT INTERRUPTIONS
• The occurrence of rapid repopulation in irradiated tumours,
sometimes with doubling times as short as 3–4 days, has
important implications for interruptions of treatment.
• Unscheduled gaps occur not infrequently in radiotherapy
schedules because of machine breakdown or patient
intercurrent illness or non-attendance.

102. TREATMENT INTERRUPTIONS
• (We shall exclude from consideration patients whose
treatment is deliberately
• stopped because of unusually severe acute reactions.)
• Gaps are important because they may lead to prolongation of
the total treatment time, allowing opportunities for rapid
repopulation for surviving tumour cells towards the end of the
schedule.

103. TREATMENT INTERRUPTIONS
• Although prolongation will often spare acute normal tissue
reactions, the risk of late effects is not reduced.
• It has been shown for squamous carcinomas of the head and
neck that reductions in cure probability of 1–2 per cent may
result from each day of prolongation..

104. TREATMENT INTERRUPTIONS
• If gaps occur, the best management strategy is ‘post-gap
acceleration’, i.e. the use of twice daily treatments (separated
by more than 6 h) or weekend treatments to enable ‘catching
up’ so that treatment is nevertheless completed within the
originally intended period.
• This does not require any changes to fraction size or total
dose.

105. TREATMENT INTERRUPTIONS
• ‘Post-gap acceleration’ may also achieved by increasing the
fraction size (hypofractionation) but this will increase the late
effect.
• However, this approach is not always feasible in practice.
• Now that the deleterious effect of prolongation is recognised,
avoidance of gaps is an important consideration for all
radiotherapy departments.

106. CHANGE IN FRACTION SIZE,
GAP CORRECTION
• A patient with colorectal cancer is planned to receive
preoperative radiotherapy with five times 5Gy from Monday
to Friday. The first two fractions are given as planned on
Monday and Tuesday, but owing to a machine breakdown, no
treatment could be given on Wednesday. In order to finish as
planned on Friday, delivering the isoeffective tumour dose by
increasing the size of the two fractions to be given on
Thursday and Friday is considered.We assume that α/β 10Gy
for colorectal cancer.

107. CHANGE IN FRACTION SIZE,
GAP CORRECTION
• Problem:
• What is the required dose per fraction for the last two
fractions? What is the accompanying change in the risk of
rectal complications from this modified fractionation
schedule?

108. CHANGE IN FRACTION SIZE,
GAP CORRECTION
• Solution:
• The tumour EQD2 for the final three fractions originally
planned is:
• We want to estimate the dose per fraction, x, so that
delivering two fractions of this size gives an EQD2 of
18.75Gy to the tumour:
Gy
GyGy
GyGy
GyEQD 75.18
102
105
152
=
+
+
=
GyGy
Gyx
xEQD
102
10
22
+
+
=

109. CHANGE IN FRACTION SIZE,
GAP CORRECTION
• By solving the above equation
• The solution to a quadratic equation of the form
• (Note that only the positive root produces a physically
meaningful dose.)
0225202
2021275.18
102
10
275.18
2
2
=−+
+=
+
+
=
xx
xx
x
x
a
acbb
x
iscbxax
2
4
0
2
2
−+−
=
=++

110. CHANGE IN FRACTION SIZE, GAP
CORRECTION
• In the present case, we get:
• In other words, we would have to give fractions of
6.7Gy on Thursday and Friday, a total of 13.4Gy, to
achieve the same tumour effect.
Gyx
x
7.6
4
9.4620
4
180040020
22
)225(242020 2
=
+−
=
++−
=

−−+−
=

111. CHANGE IN FRACTION SIZE,
GAP CORRECTION
• This is of course less than the 3 x5Gy originally planned for
Wednesday to Friday, and the reason for this is the larger
effect per gray deriving from the increased dose per fraction
in the modified schedule.

112. CHANGE IN FRACTION SIZE,
GAP CORRECTION
• How will this affect the risk of bowel damage?
• From the α/β table, α/β = 4Gy. The EQD2 of prescribed
schedule to the bowel is:
• The EQD2 of the modified schedule to the bowel is now:
5.37
6
9
25
42
45
252
==
+
+
=
GyGy
GyGy
EDQ
Gy
GyGy
GyGy
GyGy
GyGy
GyEDQ
9.389.2315
6
7.10
4.13
6
9
10
42
47.6
7.62
42
45
102
=+=+
=
+
+
+
+
+
=

113. CHANGE IN FRACTION SIZE,
GAP CORRECTION
• This means that the modified schedule has a higher complication
due to larger fraction size in the last two fraction.

114. HOWEVER, CAUTION IS
NECESSARY
• All models are just models
• The radiobiological parameters are not well known
• Parameters for a population of patients may not apply to an
individual patient